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(Color online) Viscosity η in two-dimensional space as a function of ∆t * for MPC-SR±a with θ = π/2, MPCRA±a with θ0 = π, and MPC-DR with n = 1 or n = 5. Solid and dashed lines represent analytical results for n = 5 and n = 1, respectively. (a) Symbols represent the numerical data of MPC-RA+a (, △,+), MPC-DR (•,•,⊳), MPC-RA−a (⋄,×), MPC-SR−a (), and MPC-SR+a (). Error bars are smaller than the size of symbols.
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The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multiparticle collision dynamics (MPC), and dissipative particle dynamics, are investigated, both with and without angular-momentum conservation. Analytical results are derived for fluids with an ideal-gas equation of state and a finite-time-step dynamics, a...
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... two dimensions, MPC-SR with θ = π/2 and MPC- RA with θ 0 = π are characterized by A = 1, and by B = 2 and B = 1, respectively. Thus, they have the same collisional viscosity η col for both their '−a' and '+a' ver- sion, but a different kinetic viscosity η kin , see Fig. 6. Al- though MPC-DR has the same viscosity of MPC-RA+a theoretically, the numerical data of MPC-DR shown in Fig. 3 display a slightly larger deviation from the the- oretical results for η col and a smaller deviation for η kin than the data of ...
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... This difference leads to very different behaviors in wet and dry systems. For the MPC fluid dynamics simulations, we consider a MPC variant with angular momentum conservation [47], see Supplementary Materials (SM), Sec. S-I for more details. ...
... We adopt the multiparticle collision dynamics (MPC) method [42,43], a particle-based mesoscale simulation approach, as model for the fluid. Specifically, we employ the stochastic rotation variant of MPC with angular momentum conservation (MPC-SRD+a) [47] and the celllevel Maxwell-Boltzmann scaling thermostat [60]. The algorithm consists of alternating streaming and collision steps. ...
... We use the average MPC fluid density (particles per collision cell) ⟨N c ⟩ = 20, the collision time h = 0.02a m/(k B T ) and the rotation angle α = 130 • , which yield the fluid viscosity of η = 42.6 √ mk B T /a 2 [47,65]. With the squirmer radius R c = 3a, these MPC parameters yield the rotational diffusion coefficient D R = 4.1 × 10 −5 k B T /m/a. ...
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... Since the original formulation in 1999 [28], several variants and revisions of MPC have been proposed [1], and it has been applied to a wide range of physical problems. Particularly, the transport properties of MPC fluids have been obtained theoretically [29][30][31][32][33] and its hydrodynamic correlation function has been derived [27]. The applications cover such diverse aspects as sedimenting colloidal suspensions [34,35] and polyelectrolyte electrophoresis [36], liquid crystals [37], polymeric systems and protein solutions [4,[38][39][40][41][42][43][44][45][46][47], ferro- [48] and nanofluids [49], and even self-propelled particles [50][51][52][53][54], active ne-matics [55] and active polymers [56,57], as well as biological systems such as suspensions of bacteria [14,15,[58][59][60], sperm [61][62][63], and parasites, e.g., trypanosomes [64] and Plasmodium falciparum [65]. ...
... Specifically, we use a cubic system of linear size L = 256a, and the MPC fluid density (particles per collision cell) ⟨N c ⟩ = 50, which, together with the collision time h = 0.02a m/(k B T ) and the rotation angle α = 130 • , yields the fluid viscosity of η = 111.3 √ mk B T /a 2 [32,54,68]. For squirmers, we consider the radius R c = 3a or R eff = 3.25a (see Sec. S-IV, SI), and u 0 = 0.01152 k B T /m. ...
We present HTMPC, a Heavily Templated C++ library for large-scale simulations implementing multi-particle collision dynamics (MPC), a particle-based mesoscale hydrodynamic simulation method. The implementation is plugin-based, and designed for distributed computing over an arbitrary number of MPI ranks. By abstracting the hardware-dependent parts of the implementation, we provide an identical application-code base for various architectures, currently supporting CPUs and CUDA-capable GPUs. We have examined the code for a system of more than a trillion MPC particles distributed over a few thousand MPI ranks (GPUs), demonstrating the scalability of the implementation and its applicability to large-scale hydrodynamic simulations. As showcases, we examine passive and active suspension of colloids, which confirms the extensibility and versatility of our plugin-based implementation.
... Besides the time step Δt which determines the mean-free path = Δt √ k B T∕m , the mean number of particles per collision cell Q is the other crucial parameter in the MPC model (Malevanets and Kapral 1999;Noguchi and Gompper 2008). Due to the importance ...
... of angular momentum conservation, we here follow our earlier work ) and implement the angular momentum-conserving algorithm (denoted as MPC-DR in Ref. Noguchi and Gompper 2008), where the rotation angle is not a free parameter but chosen as ...
... Furthermore, to study self-diffusion in an unbounded domain, we consider in this section a periodic system without any walls present. Under these conditions and for the two-dimensional angular momentum-conserving collision model adopted here, the diffusion coefficient was calculated using molecular chaos assumption (Noguchi and Gompper 2008) as Figure 1a shows the diffusion coefficient as a function of the average number of MPC particles per collision cell Q for two selected temperatures. ...
As more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.
... ffiffiffiffiffiffiffiffiffiffiffi ffi mk B T p =a, according to ref. 68 . The rotors are modelled as impenetrable moving and rotating no-slip boundaries that exchange linear and angular momentum with the fluid in the streaming step and in the collision step, by introducing virtual particles 39,40 . ...
Active fluids display collective phenomena such as active turbulence or odd viscosity, which refer to spontaneous complex and transverse flow. The simultaneous emergence of these seemingly separate phenomena is here reported in experiment for a chiral active fluid composed of a carpet of standing and spinning colloidal rods, and in simulations for synchronously rotating hard discs in a hydrodynamic explicit solvent. Experiments and simulations reveal that multi-scale eddies emerge, a hallmark of active turbulence, with a power-law decay of the kinetic-energy spectrum, a feature of self-similar dynamics. Moreover, the particles are dragged to the centre of the vortices, a telltale sign of odd viscosity. The weak compressibility of the system enables an explicit measurement of the odd viscosity in bulk via the relation between local vorticity and excess density. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.
... A total of N C = 20 fluid particles were used per cell and the MPCD timestep was chosen as δt = 10 −2 τ MPCD , whereas the MD timestep is δt MD = 10 −4 τ MPCD , where τ MPCD = ma 2 /(k B T ) is the unit of time in the MPCD simulation. The kinematic viscosity ν = η/ρ of the fluid for the MPC-AT+a algorithm (including both kinetic and collisional contribution) is then given by ν = 3.88a k B T /m [35,61,65]. The energy scale for steric interaction was chosen as = 200k B T . ...
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... The pure MPC fluid is obtained in this scheme for the special case of setting the number density n = 0, thereby switching off magnetic contributions to hydrodynamics since in this case T pot = f M = 0 and T vis = 2η s D. Analyzing the particles' mean-squared displacements r 2 i (t ) , we find a linear relation r 2 i (t ) = 6D s t from which we determine D s . Good agreement of our simulation results with the theoretical prediction D s = (k B T t/m)[Q/(Q − 2) − 1/2] is seen in Fig. 1(a) for large enough Q, for which the theoretical result was derived [46]. ...
Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.
... This dynamics conserves both local linear and angular momentum [32,33] and keeps the temperature constant [34]. The viscosity of the fluid is given by [35] ...
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient). The suspension viscosity is found to be a monotonous increasing function of the viscosity contrast (the ratio of the viscosity of the encapsulated fluid to that of the surrounding fluid) both in the tank-treading and the tumbling regime due to the interplay of different temperature-depending mechanisms. Thermal effects induce shape and inclination fluctuations of the vesicle which experiences also Brownian diffusion across the channel increasing the viscosity. These effects reduces when increasing the Peclet number.
... This dynamic conserves both local linear and angular momentum [32,33] and keeps the temperature constant [34]. The viscosity of the fluid is given by [35] ...
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient). The suspension viscosity is found to be a monotonous increasing function of the viscosity contrast (the ratio of the viscosity of the encapsulated fluid to that of the surrounding fluid) both in the tank-treading and the tumbling regime due to the interplay of different temperature-depending mechanisms. Thermal effects induce shape and inclination fluctuations of the vesicle which also experiences Brownian diffusion across the channel increasing the viscosity. These effects reduce when increasing the Peclet number.
... the system, which is compensated by considering a thermostat in each time step to all collision boxes individually, 63 becoming also a guarantee of a constant system temperature k B T. For the fluid, we employ an average number of particles per collision cell n = 10 and take the collision time, i.e., the time between two collisions, as h = 0.02a m/(k B T), yielding a viscosity of η = 17.9 √ mk B T/a, according to reference. 62 The rotors are modelled as impenetrable moving and rotating noslip boundaries that exchange linear and angular momentum with the fluid in the streaming step and in the collision step, by introducing virtual particles. 36,37 From the mean squared displacement in Figure 6d, the diffusion coefficient in the dilute regime can be determined to be D = 3.73 × 10 −4 σ 2 /(a m/(k B T)). ...
The simultaneous emergence of active turbulence and odd viscosity for a colloidal rotors system is here shown. Rod-like colloidal particles with a ferromagnetic head and magnetic moment perpendicular to the rod axis, precess vertically to the substrate under an externally rotating field. The colloid rotation drags the adjacent fluid inducing the translation of neighbouring colloids, behaviour which is also captured by hydrodynamic simulations of discs rotating in sync. Experiments and simulations reveal that multi-scale eddies emerge with an energy spectrum following a power-law decay: this feature of self-similar dynamics without the emergence of a dominant vortex size is characteristic of active turbulence. Moreover, the particles are dragged to the center of the vortices, a telltale sign of systems with odd viscosity, which is explicitly measured. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.
... Here, the particles are sorted into the cells of a cubic lattice of mesh size a that defines the local interaction environment. The velocities of the fluid particles after the collision, vi(t + h), are given by 47,48 vi ...
... within the stochastic rotation dynamics (SRD) variant of MPC, with local linear and angular momentum conservation (MPC-SRD+a). 5,47 Here, R(α) is the rotation matrix for the rotation of the relative velocities vi,cm = vi − vcm with respect to the cell's centerof-mass velocity vcm, where the ith particle belongs to. The rotation is performed around a randomly oriented axis by a fixed angle α. 49 The axis orientation is chosen independently for every cell and for every collision step. ...
The properties of microswimmer dumbbells composed of pusher-puller pairs are investigated by mesoscale hydrodynamic simulations employing the multiparticle collision dynamics approach for the fluid. An individual microswimmer is represented by a squirmer, and various active-stress combinations in a dumbbell are considered. The squirmers are connected by a bond, which does not impose any geometrical restriction on the individual rotational motion. Our simulations reveal a strong influence of the squirmers' flow fields on the orientation of their propulsion directions, their fluctuations, and the swimming behavior of a dumbbell. The properties of pusher-puller pairs with equal magnitude of the active stresses dependent only weakly on the stress magnitude. This is similar to dumbbells of microswimmers without hydrodynamic interactions. However, for non-equal stress magnitudes, the active stress implies strong orientational correlations of the swimmers' propulsion directions with respect to each other as well as the bond vector. The orientational coupling is most pronounced for pairs with large differences of the active stress magnitude. The alignment of the squirmer propulsion directions with respect to each other is preferentially orthogonal in dumbbells with a strong pusher and weak puller, and antiparallel in the opposite case when the puller dominates. These strong correlations affect the active motion of dumbbells which is faster for strong pushers and slower for strong pullers.
